It has been a quirk of the FA Cup's velvet bag and numbered balls ritual that Manchester City's meeting with Chelsea in Sunday's semi-final is the pair's first in the competition for 42 years – and only the fourth since Gus and Joseph Mears purchased Stamford Bridge in 1904 and founded the club they had initially pondered calling London FC the following spring. By contrast, since that fourth-round tie in January 1971 Manchester United have been drawn to play Arsenal nine times and Chelsea seven times, while Mancunians have also been treated to five Cup derbies.

Not that the rarity value adds greater spice to the meeting of two sides wholly transformed by the largesse of billionaire investment from the significantly more parochially run First Division clubs of five decades ago. During the week of the tie in 1971 Chelsea had spent £475,000 to buy the freehold of Stamford Bridge from the JT Mears Trustees and announced a 10-year plan of refurbishment intended to transform the ramshackle old stadium, still bordered at either end by cavernous terraces with the dog-track lights ringing the pitch, into an 80,000 all-seat ground, the first in Europe. The original estimates proved hopelessly optimistic and, although the East Stand was rebuilt as a three-tier ugly-chic carbuncle with hideous brown seats, escalating costs and mid-70s inflation spikes saddled the board with such debts that Ken Bates was able to purchase the club, if not the ground, for £1 in 1982, the year the Bridge was supposed to be ready to host 80,000 fans and treat them to heated seats, gourmet restaurants and electronic scoreboards.

Chelsea's defence of the Cup began with a 2-2 draw with Crystal Palace on a treacherously icy Selhurst Park pitch but they recovered their verve for a comfortable 2-0 victory in the replay. Manchester City had a comparatively easy draw against Wigan Athletic, then in the Northern Premier League, but laboured to win 1-0 after a weak kick by Wigan's goalkeeper Dennis Reeves, a semi-professional and painter and decorator, gave City's relentless dynamo Colin Bell the opportunity to score. Although City were third in Division One and Chelsea one point behind them in fifth, their form had been patchy. Defensively they had been miserly but City's nine draws from 25 games and Chelsea's 10 from the same number had left them trailing the leaders, Leeds United, by 10 and 11 points, an embarrassingly substantial gap in the era of two points for a win.

A crowd of more than 55,000 had witnessed Chelsea's midweek victory over Palace but heavy rain dashed the board's hopes of hitting the capacity against City, though disappointment at an attendance of 50,176 would make most clubs feel wistful in the decades since. The visitors, with their artful and ruthless centre-forward Francis Lee injured, sent out George Heslop in the No7 shirt but stationed him in the heart of defence alongside Tommy Booth to counter the subtle skill of Chelsea's Peter Osgood and the rather more bludgeoning approach of his partner, Ian Hutchinson. Osgood was playing his last game before starting an eight-week ban for accruing six bookings and began with the determination of someone bridling at the injustice of two months' enforced idleness. Yet Heslop stuck to his assignment and with a mixture of luck, skill and judgment held him at bay.

Osgood's greatest skills were his delicate touch and ability to discern defensive weaknesses and one can picture him in his straight-backed guardsman's pose, sniffing out faultlines like a Frenchman smelling for ripeness in melons. First he set Hutchinson through on goal but City's left-back, Arthur Mann, read his thoughts and made a nimble intervention, then a glorious reverse pass wrongfooted the defence but Peter Houseman, stealing in from the left, smashed his shot wide.

City, weakened by injuries, but following the old military motto that irregulars always work harder for their medals, had packed the midfield with the teenagers Ian Bowyer and Derek Jeffries bolstering Mike Doyle, Alan Oakes and Bell leaving Mike Summerbee as a solo forward. It left them lacking invention in the first-half but ultimately succeeded in drawing Chelsea's sting.

The game changed nine minutes after the break when Bell, pushed forward because Summerbee had to be replaced by Neil Young at the interval, was gifted possession by David Webb's hapless miskick and calmly rolled his shot underneath Peter Bonetti's urgent dive. Two minutes later he scored again, powerfully and precisely steering in Young's low cross at the far post after the Chelsea centre-half Marvin Hinton let it run past him thinking no one was outside. Bell's stamina and tenacity were celebrated in his nickname "Nijinsky" – after the triple crown-winning thoroughbred rather than the male principal of the Ballet Russes – but arguably the greatest danger he posed to the opposition was his sheer athletic elusiveness.

"Crumbs," says the Chelsea midfielder John Hollins. "Everyone will think it was me supposed to be marking Colin that day as I usually did. But he'd gone up front. He was a riot to play against. You had to have the energy of three men even to try to outwork him. You would be playing against him and all of a sudden you would be looking over your shoulder, thinking: 'Where did he go?' He was a phenomenon."

Bowyer scored City's third and confirmed that Chelsea, who had had to go to Manchester to win the Cup (in a replay against Leeds), would lose it to a team from the city of their triumph. But it proved a pyrrhic victory for City, who were knocked out in the next round by the eventual Double-winners, Arsenal, as the battle for control of the team between their manager, Joe Mercer, and his innovative, charismatic if impatient coach, Malcolm Allison, began to spiral towards open warfare. "Dare I say it?" says Hollins. "But the prize, having won the FA Cup the previous season, we perhaps took a little lightly. The Cup Winners' Cup seemed a bigger goal for us that season."

In the semi-final of that competition, as fate would have it, Chelsea were drawn against the holders, Manchester City, defeated them 1-0 in both legs and went on to win the final in a replay against Real Madrid.

For Hollins there was another cherished victory 15 years later when, as Chelsea's manager, he led them to a 5-4 victory over City in the Full Members Cup in 1986, the sides' only previous match at Wembley. That tournament, introduced after English clubs were banned from Europe following Heysel, was so maltreated by the Football League that both played matches on the Saturday, 24 hours before the final. Chelsea led 5-1 with six minutes to go before City almost pulled off a remarkable comeback. "There wasn't a game like it at Wembley since the Matthews final," says Hollins. "Everybody enjoyed it but I didn't. I was sweating by the end. It was the time when people were saying that football was dying. If so, I said, I hope it's dying like that."

On Sunday, just like in 1971, Chelsea, the holders, take on their immediate predecessors as Cup winners. "We've got so many goalscorers in the team," says Hollins, "and look at [Sergio] Agüero, he's back in top form. Could it be 5-4 again? I hope so. City v Chelsea has always been one hell of a game."